If the numerical coefficient of the pth term in expansion of (2x+3)^6 is 4860,then value of p is/are?

pth term in the expansion of $(2x+3{)}^6 is {}^{6}C_{p-1}.(2x{)}^{6-(p-1)}.3^{p-1}$
$={}^{6}C_{p-1}.2^{7-p}.3^{p-1}.x^{7-p}$ .......(1)

let us find the factor of 4860 ; $4860=2^2*3^5*5$ .......(2)
the maximum exponent of 3 which will divide ${}^{6}C_r$ is 2.

now comparing the exponent of 3 from (1) and (2):
now for p -1=5 , i.e. p=6 the numerical coefficient  is ${}^{6}C_5.2^1.3^5$

for p-1 = 4 i.e. p =5
the numerical coefficient is ${}^{6}C_4.2^2.3^4=\frac{6*5}{2}*4*81=2^2*3^5*5$
therefore numerical coefficient of 5th term is 4860.

hope this helps you